One of the extras in the GOG version are extra levels, and one set, huntbgn2, is described thusly according to the readme file:
"1) Huntbgn2.rtl / Huntbgn2.rtc
Back in early 1995 when Rise of the Triad was a new game, there was a
special shareware version of the game produced entitled "Rise of the
Triad: The HUNT Begins Deluxe Edition". The game itself was the same,
the only difference between the regular shareware and the deluxe was the
inclusion of 6 additional levels (3 regular & 3 Comm-bat) in the deluxe
version that never appeared in any other variant of the game. The six
levels are entitled:

Regular : Prelude to a Kill, Jumpin Jehoshapat, & Gadzooks!
Comm-Bat: The Siege, The Box, Rise & Tide

All 6 levels were designed by Tom Hall, and you can use these either on
your registered Rise of the Triad game, or on the shareware edition.
The other levels in these level packs are the existing shareware levels
- these extras are in addition to the shareware levels that are already
in your game."

So you'll have to unpack these extra levels into the game and use the setup utility to load the extra levels. As far as I can tell from playing, it's as the readme described, the shareware levels plus extra maps.